e-h pairs are generated everywhere,
but...
Subscript "0"
means no light.
---------------------------
VOC
-V
(Not necessarily population inversion)
Where does the recombination
primarily happen?
What do you already know about lasers?
(How are lasers different from other light
sources?)
http://www.ecse.rpi.edu/~schubert/Light-Emitting-Diodes-dot-org/chap07/chap07.htm
E2
These two energies
are not independent.
Related by a fixed
difference -- the
photon energy.
E1
fc
-f v
_______
not important
(The probability of having a hole)
(stimulated
________ emission more likely than absorption)
n
What's needed in a pn junction for
population inversion?
Eg
Efn - E fp
Double heterojunction laser
http://zone.ni.com/devzone/cda/ph/p/id/249
612
SEMICONDUCTOR PHOTON SOURCES
",{ v)
tc {v)
+1~------------~'-
f,(ll): je-(V) - flA(lI)
fc (b~) f
-
\
\
\
v (bd
hv
\
- 1
Figure 16.2-2 Dependence on energy of the
joint optical density of states Q( lI ), the Fermi
inversion factor f/lI) , and the gain coefficient
Yo(lI) at T = 0 K (solid curves) and at room
temperature (dashed curves). Photons whose en­
ergy lies between Eg and Ef c - Ef u undergo laser
amplification.
Gain!
o~----~--------~--~
Loss
Eg
\
\
\
\
\
hv
~
Computation of the gain properties is simplified considerably if thermal
can be ignored (viz., T = 0 K). The Fermi functions are then simply !/E 2 ) = 1
E2 < Ef c and 0 otherwise; ! u(E 1) = 1 for EI < Ef u and 0 otherwise. In that case
Fermi inversion factor is
!(1I)={+1,
g
-1,
hll
< Efc - Ef u
otherwise.
Schematic plots of the functions Q(II), !gCII), and the gain coefficient YO(II)
presented in Fig. 16.2-2, illustrating how YO(II) changes sign and turns into a
coefficient when hll > Ef c - Ef u. The 11- 2 dependence of YO(II), arising from the
factor in the numerator of 06.2-4), is sufficiently slow that it may be ignored.
temperature smoothes the functions !g(lI) and YO(II), as shown by the dashed
Fig. 16.2-2.
Dependence of the Gain Coefficient on Pumping Level
The gain
) increases both in its
dth and
1-1 a consta
(number of inje~d excess electron-hole pairs per cm 3 per second)
steady-state concentration of injected electron-hole pairs in accordance
= RT , where T is the electron-hole recombination lifetime (which
railiative and nonradiative contributions). Knowledge of the steady-steady
centrations of electrons and holes, " = "0 + il" and p = Po + il", respective!y,
the Fermi levels E c and E
dete ' ed via 6.1-7 . Once the Fenm
known, the
m ratIOn of the gain coefficient can proceed using (
~-.*
~
ett-A ~,,(j'V>
.
~~,
Q.
~v,
g is the gain/loss associated
with the transitions across
the band gap.
Here, "loss" is loss other than -g, which sets
the threshold.